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<meta name="description" content="第二章 线性表线性表：表内数据类型相同，有限序列 本章将以总结的形式展现： 2.1 顺序表与链式表的区别     顺序表 链式表     存取 随机存取 顺序存取   结构 顺序存储（连续） 随机存储（不连续）   空间分配 静态存储（可以动态分配） 动态存储   操作 查找 O(1) ,插入和删除O（n） 查找 O(n) ,插入和删除O（1）   缺点 插入删除不便，长度不可以改变 查找速度慢，">
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<meta property="og:description" content="第二章 线性表线性表：表内数据类型相同，有限序列 本章将以总结的形式展现： 2.1 顺序表与链式表的区别     顺序表 链式表     存取 随机存取 顺序存取   结构 顺序存储（连续） 随机存储（不连续）   空间分配 静态存储（可以动态分配） 动态存储   操作 查找 O(1) ,插入和删除O（n） 查找 O(n) ,插入和删除O（1）   缺点 插入删除不便，长度不可以改变 查找速度慢，">
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        <h1 class="article-title">贝叶斯</h1>
    
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            Created At : <time class="date" title='Updated At: 2020-08-09 14:28:07'>2019-08-04 08:50</time>
        
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        <ol class="toc"><li class="toc-item toc-level-2"><a class="toc-link" href="#%E9%80%9A%E8%BF%87%E6%9C%AC%E6%96%87%EF%BC%8C%E4%BD%A0%E5%BA%94%E8%AF%A5%E5%AD%A6%E4%BC%9A%EF%BC%9A"><span class="toc-text">通过本文，你应该学会：</span></a></li></ol></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E6%A0%B8%E5%BF%83%E7%AE%97%E6%B3%95"><span class="toc-text">核心算法</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#%E8%B4%9D%E5%8F%B6%E6%96%AF%E5%85%AC%E5%BC%8F"><span class="toc-text">贝叶斯公式</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E5%85%A8%E6%A6%82%E7%8E%87%E5%85%AC%E5%BC%8F%EF%BC%9A"><span class="toc-text"> 全概率公式：</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E6%9D%A1%E4%BB%B6%E6%A6%82%E7%8E%87"><span class="toc-text">条件概率</span></a></li></ol></li></ol></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E8%B4%9D%E5%8F%B6%E6%96%AF%E5%88%86%E7%B1%BB%E5%99%A8%E6%8E%A8%E5%AF%BC%E8%BF%87%E7%A8%8B"><span class="toc-text">贝叶斯分类器推导过程</span></a></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E7%AE%97%E6%B3%95%E6%AD%A5%E9%AA%A4"><span class="toc-text">算法步骤</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#1%E3%80%81%E7%A1%AE%E5%AE%9A%E7%89%B9%E5%BE%81%E5%B1%9E%E6%80%A7%E5%8F%8A%E5%88%92%E5%88%86"><span class="toc-text">1、确定特征属性及划分</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#2%E3%80%81%E8%8E%B7%E5%8F%96%E8%AE%AD%E7%BB%83%E6%A0%B7%E6%9C%AC"><span class="toc-text">2、获取训练样本</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#3%E3%80%81%E8%AE%A1%E7%AE%97%E8%AE%AD%E7%BB%83%E6%A0%B7%E6%9C%AC%E4%B8%AD%E6%AF%8F%E4%B8%AA%E7%B1%BB%E5%88%AB%E7%9A%84%E9%A2%91%E7%8E%87"><span class="toc-text">3、计算训练样本中每个类别的频率</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#4%E3%80%81%E8%AE%A1%E7%AE%97%E6%AF%8F%E4%B8%AA%E7%B1%BB%E5%88%AB%E6%9D%A1%E4%BB%B6%E4%B8%8B%E5%90%84%E4%B8%AA%E7%89%B9%E5%BE%81%E5%B1%9E%E6%80%A7%E5%88%92%E5%88%86%E7%9A%84%E9%A2%91%E7%8E%87"><span class="toc-text">4、计算每个类别条件下各个特征属性划分的频率</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#5%E3%80%81%E4%BD%BF%E7%94%A8%E5%88%86%E7%B1%BB%E5%99%A8%E8%BF%9B%E8%A1%8C%E9%89%B4%E5%88%AB"><span class="toc-text">5、使用分类器进行鉴别</span></a></li></ol></li></ol></li><li class="toc-item toc-level-1"><a class="toc-link" href="#4-%E7%AE%80%E5%8D%95%E5%BA%94%E7%94%A8"><span class="toc-text">4.简单应用</span></a><ol class="toc-child"><li class="toc-item toc-level-4"><a class="toc-link" href="#%E8%A6%81%E6%B1%82-Rain%EF%BC%8CHot%EF%BC%8CHigh%EF%BC%8CWeak%E7%9A%84%E5%A4%A9%E6%B0%94%E9%80%82%E4%B8%8D%E9%80%82%E5%90%88play-tennis"><span class="toc-text">要求 Rain，Hot，High，Weak的天气适不适合play tennis?</span></a></li></ol></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E6%8B%89%E6%99%AE%E6%8B%89%E6%96%AF%E5%B9%B3%E6%BB%91%EF%BC%9A"><span class="toc-text">拉普拉斯平滑：</span></a></li></ol></li></ol></li><li class="toc-item toc-level-1"><a class="toc-link" href="#5-%E7%AE%97%E6%B3%95%E4%BC%98%E7%BC%BA%E7%82%B9"><span class="toc-text">5.算法优缺点</span></a></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E5%B0%8F%E7%BB%93"><span class="toc-text">小结</span></a><ol class="toc-child"><li class="toc-item toc-level-5"><a class="toc-link" href="#1-%E8%B4%9D%E5%8F%B6%E6%96%AF%E5%85%AC%E5%BC%8F%E7%9A%84%E4%BC%98%E7%BC%BA%E7%82%B9%E7%96%91%E9%97%AE%EF%BC%9A%E8%83%BD%E8%AF%B4%E5%87%BA%E8%BF%99%E4%BA%9B%E4%BC%98%E7%BC%BA%E7%82%B9%E8%83%8C%E5%90%8E%E7%9A%84%E5%8E%9F%E5%9B%A0%E4%B9%88%EF%BC%9F"><span class="toc-text">1.贝叶斯公式的优缺点疑问：能说出这些优缺点背后的原因么？</span></a></li></ol></li></ol></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E5%B8%A6%E4%BD%A0%E6%90%9E%E6%87%82%E6%9C%B4%E7%B4%A0%E8%B4%9D%E5%8F%B6%E6%96%AF%E5%88%86%E7%B1%BB%E7%AE%97%E6%B3%95"><span class="toc-text">带你搞懂朴素贝叶斯分类算法</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E7%90%86%E8%A7%A3%E8%B4%9D%E5%8F%B6%E6%96%AF%E5%AE%9A%E7%90%86"><span class="toc-text">理解贝叶斯定理</span></a></li></ol></li></ol>
    
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        <h2 id="通过本文，你应该学会："><a href="#通过本文，你应该学会：" class="headerlink" title="通过本文，你应该学会："></a>通过本文，你应该学会：</h2><p>先验事件与后验事件</p>
<p>条件概率</p>
<p>二级概率</p>
<p>空间样本</p>
<p>贝叶斯公式</p>
<p>拉普拉斯平滑</p>
<a id="more"></a>
<h1 id="核心算法"><a href="#核心算法" class="headerlink" title="核心算法"></a>核心算法</h1><h3 id="贝叶斯公式"><a href="#贝叶斯公式" class="headerlink" title="贝叶斯公式"></a>贝叶斯公式</h3><p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190823221025.png" alt=""></p>
<p>推导过程可以由两个条件公式推出</p>
<!--more-->
<p>公式的含义？</p>
<p>​                        <img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190823221039.png" alt=""></p>
<p>从数学角度来说，分类问题可做如下定义：已知集合<img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190823221354.png" alt="">和<img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190823221419.png" alt="">，确定映射规则y = f(x)，使得任意xi有且仅有一个yi,使得<img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190823221534.png" alt="">成立。</p>
<p>该算法的内容，就是要求给定特征————&gt;&gt;&gt;&gt;让我们得出类别，这也是所有问题的关键，</p>
<h3 id="全概率公式："><a href="#全概率公式：" class="headerlink" title=" 全概率公式："></a><a target="_blank" rel="noopener" href="https://baike.baidu.com/item/全概率公式"> 全概率公式</a>：</h3><p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190823221055.png" alt=""></p>
<p>全概率公式为<a target="_blank" rel="noopener" href="https://baike.baidu.com/item/%E6%A6%82%E7%8E%87%E8%AE%BA/829122">概率论</a>中的重要公式，它将对一复杂事件A的概率求解问题转化为了在不同情况下发生的简单事件的概率的求和问题。该公式可以理解为P(A)=P(A|B1)P(B1) + P(A|B2)P(B2) + … + P(A|Bn)P(Bn)</p>
<p>通俗理解，就是发生A的概率，就是在任何情况下发生A的概率</p>
<h3 id="条件概率"><a href="#条件概率" class="headerlink" title="条件概率"></a>条件概率</h3><p>P<em>(</em>A<em>∣</em>B<em>)=</em>P<em>(A</em>B<em>)</em>/P<em>(</em>B)</p>
<h1 id="贝叶斯分类器推导过程"><a href="#贝叶斯分类器推导过程" class="headerlink" title="贝叶斯分类器推导过程"></a>贝叶斯分类器推导过程</h1><p>两个条件概率</p>
<h1 id="算法步骤"><a href="#算法步骤" class="headerlink" title="算法步骤"></a>算法步骤</h1><p>首先设C=0表示真实账号，C=1表示不真实账号。</p>
<h3 id="1、确定特征属性及划分"><a href="#1、确定特征属性及划分" class="headerlink" title="1、确定特征属性及划分"></a>1、确定特征属性及划分</h3><p>这一步要找出可以帮助我们区分真实账号与不真实账号的特征属性，在实际应用中，特征属性的数量是很多的，划分也会比较细致，但这里为了简单起见，我们用少量的特征属性以及较粗的划分，并对数据做了修改。</p>
<p>我们选择三个特征属性：a1：日志数量/注册天数，a2：好友数量/注册天数，a3：是否使用真实头像。在SNS社区中这三项都是可以直接从数据库里得到或计算出来的。</p>
<p>下面给出划分：a1：{a&lt;=0.05, 0.05<a<0.2, a>=0.2}，a1：{a&lt;=0.1, 0.1<a<0.8, a>=0.8}，a3：{a=0（不是）,a=1（是）}。</p>
<h3 id="2、获取训练样本"><a href="#2、获取训练样本" class="headerlink" title="2、获取训练样本"></a>2、获取训练样本</h3><p>这里使用运维人员曾经人工检测过的1万个账号作为训练样本。</p>
<h3 id="3、计算训练样本中每个类别的频率"><a href="#3、计算训练样本中每个类别的频率" class="headerlink" title="3、计算训练样本中每个类别的频率"></a>3、计算训练样本中每个类别的频率</h3><p>用训练样本中真实账号和不真实账号数量分别除以一万，得到：</p>
<h3 id="4、计算每个类别条件下各个特征属性划分的频率"><a href="#4、计算每个类别条件下各个特征属性划分的频率" class="headerlink" title="4、计算每个类别条件下各个特征属性划分的频率"></a>4、计算每个类别条件下各个特征属性划分的频率</h3><h3 id="5、使用分类器进行鉴别"><a href="#5、使用分类器进行鉴别" class="headerlink" title="5、使用分类器进行鉴别"></a>5、使用分类器进行鉴别</h3><h1 id="4-简单应用"><a href="#4-简单应用" class="headerlink" title="4.简单应用"></a>4.简单应用</h1><p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190823221318.png" alt=""></p>
<h4 id="要求-Rain，Hot，High，Weak的天气适不适合play-tennis"><a href="#要求-Rain，Hot，High，Weak的天气适不适合play-tennis" class="headerlink" title="要求 Rain，Hot，High，Weak的天气适不适合play tennis?"></a>要求 Rain，Hot，High，Weak的天气适不适合play tennis?</h4><p>Outlook 三种属性 及各自概率</p>
<p>Temperature 三种属性及各自概率</p>
<p>Humidity 两种属性 及各自概率</p>
<p>风力两种属性及各自概率</p>
<p>根据公式：P（Yes/X）=P(X/Yes)<code>*</code>p(yes)/p(X)  =  P((Rain，Hot，High，Weak)/Yes)<code>*</code>P(Yes)/p(Rain，Hot，High，Weak)</p>
<p>由于假设了四种属性相互独立：P（Yes/X）=四种属性分开概率相乘</p>
<p>同理，求出P（No/X）</p>
<p>比较 P（Yes/X）与P（No/X），谁大就是谁</p>
<p>若是单纯为了比肩两者，分母可以不带</p>
<p>（也可以引入拉普帕斯平滑）</p>
<h3 id="拉普拉斯平滑："><a href="#拉普拉斯平滑：" class="headerlink" title="拉普拉斯平滑："></a>拉普拉斯平滑：</h3><p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190823221334.png" alt=""></p>
<p><strong>为什么要进行</strong>？</p>
<p>零概率问题，就是在计算实例的概率时，如果某个量x，在观察样本库（训练集）中没有出现过，会导致整个实例的概率结果是0。在文本分类的问题中，<strong>当一个词语没有在训练样本中出现，该词语调概率为0，使用连乘计算文本出现概率时也为0。这是不合理的，不能因为一个事件没有观察到就武断的认为该事件的概率是0。</strong></p>
<p>（带有拉普拉斯平滑的解答：<a target="_blank" rel="noopener" href="https://blog.csdn.net/x_iunknown/article/details/82898503）">https://blog.csdn.net/x_iunknown/article/details/82898503）</a></p>
<h1 id="5-算法优缺点"><a href="#5-算法优缺点" class="headerlink" title="5.算法优缺点"></a>5.算法优缺点</h1><p>朴素贝叶斯的主要优点有：</p>
<p>（1）算法简单，有稳定的效率。</p>
<p>（2）对小规模的数据表现很好，能处理多分类任务，9是和增加训练，尤其是数据超出内初时我们可以一批批的去增加训练</p>
<p>（3）对缺失的数据不太敏感</p>
<p>缺点：</p>
<p>（1）假设如果与实际不符，会影响模型效果</p>
<p>（2）输入数据的表现形式，比如是连续特征，离散特征还是二元特征，会影响分类效果。</p>
<h1 id="小结"><a href="#小结" class="headerlink" title="小结"></a>小结</h1><h5 id="1-贝叶斯公式的优缺点疑问：能说出这些优缺点背后的原因么？"><a href="#1-贝叶斯公式的优缺点疑问：能说出这些优缺点背后的原因么？" class="headerlink" title="1.贝叶斯公式的优缺点疑问：能说出这些优缺点背后的原因么？"></a>1.贝叶斯公式的优缺点<strong><em>疑问：能说出这些优缺点背后的原因么？</em></strong></h5><p>2.贝叶斯分类的算法</p>
<p>3.拉普拉斯平滑的作用</p>
<p>更多：</p>
<h3 id="带你搞懂朴素贝叶斯分类算法"><a href="#带你搞懂朴素贝叶斯分类算法" class="headerlink" title="带你搞懂朴素贝叶斯分类算法"></a><a target="_blank" rel="noopener" href="https://blog.csdn.net/amds123/article/details/70173402">带你搞懂朴素贝叶斯分类算法</a></h3><h3 id="理解贝叶斯定理"><a href="#理解贝叶斯定理" class="headerlink" title="理解贝叶斯定理"></a><a target="_blank" rel="noopener" href="https://zhuanlan.zhihu.com/p/45432367">理解贝叶斯定理</a></h3>
      
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